In the Singapore scenario the intention is that neither tanks not artillery may enter the Johore Strait. So the only way the tanks can get ashore on Singapore Island is via a repaired Causeway.

This presents both players with a number of choices. The Japanese player may want to get the tanks ashore to support the final push, but may lose a tempo in the process if too many orders go to the engineers. Similarly the British may find the Japanese in their rear areas sooner than expected if they spend too much effort trying to stop the engineers. As someone has already pointed out, the Japanese can win without the tanks...

My apologies for the lack of clarity. Nothing to do with the guys at DoW!

So do we actually need to give an order to the engineers to repair the bridge?

Just quoting: "After playing a Command Card and before any units are ordered..." - I deduce from this wording that they automatically repair the bridge.

The first time I played the scenario I wasted a LOT of rolls on repairing instead of attacking the Tommies...

I played it like sabotage or night rules. The dice were rolled without an order/ just as a routine roll at the beginning of the Axis turn ( as long as the engineer was on the bridge hex).